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Article Dans Une Revue Journal of the European Mathematical Society Année : 2002

Green's generic syzygy conjecture for curves of even genus lying on a K3 surface

Claire Voisin
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Résumé

We consider the generic Green conjecture on syzygies of a canonical curve, and particularly the following reformulation thereof: {\it For a smooth projective curve $C$ of genus $g$ in characteristic 0, the condition ${\rm Cliff} C>l$ is equivalent to the fact that $K_{g-l'-2,1}(C,K_C)=0, \forall l'\leq l$.} We propose a new approach, which allows up to prove this result for generic curves $C$ of genus $g(C)$ and gonality ${\rm gon(C)}$ in the range $$\frac{g(C)}{3}+1\leq {\rm gon(C)}\leq\frac{g(C)}{2}+1.$$

Dates et versions

hal-00021784 , version 1 (25-03-2006)

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Claire Voisin. Green's generic syzygy conjecture for curves of even genus lying on a K3 surface. Journal of the European Mathematical Society, 2002, 47, pp.363-404. ⟨hal-00021784⟩
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